The Oxford Handbook of Random Matrix Theory

by Akemann, Gernot; Baik, Jinho; Di Francesco, Philippe

• ISBN13: 9780199574001
• ISBN10: 0199574006
• Format: Hardcover
• Copyright: 2011-09-25
• Publisher: Oxford University Press

Summary

With a foreword by Freeman Dyson, the handbook brings together leading mathematicians and physicists to offer a comprehensive overview of random matrix theory, including a guide to new developments and the diverse range of applications of this approach. In part one, all modern and classical techniques of solving random matrix models are explored, including orthogonal polynomials, exact replicas or supersymmetry. Further, all main extensions of the classical Gaussian ensembles of Wigner and Dyson are introduced including sparse, heavy tailed, non-Hermitian or multi-matrix models. In the second and larger part, all major applications are covered, in disciplines ranging from physics and mathematics to biology and engineering. This includes standard fields such as number theory, quantum chaos or quantum chromodynamics, as well as recent developments such as partitions, growth models, knot theory, wireless communication or bio-polymer folding. The handbook is suitable both for introducing novices to this area of research and as a main source of reference for active researchers in mathematics, physics and engineering.

Table of Contents

Forward

Introduction

Guide to the Handbook

History

Properties of Random Matrix Theory

Symmetry Classes

Spectral Statisitics of Unitary Emsembles

Spectral Statistics of Orthogonal and Symplectic Ensembles

Universality

Supersymmetry

Replica Approach

Painleve Transcendents

Random Matrices and Integrable Systems

Determinantal Point Processes

Random Matrix Representations of Critical Statistics

Heavy-Tailed Random Matrices

Phase Transitions

Two-Matrix Models and Biorthogonal Polynomials

Loop Equation Method

Unitary Integrals and Related Matrix Models

Non-Hermitian Ensembles

Characteristic Polynomials

Beta Ensembles

Wigner Matrices

Free Probability Theory

Random Banded and Sparse Matrices

Applications of Random Matrix Theory

Number Theory

Random Permutations

Enumeration of Maps

Knot Theory

Multivariate Statistics

Algrebraic Geometry

Two-Dimensional Quantum Gravity

String Theory

Quantum Chromodynamics

Quantum Chaos and Quantum Graphs

Resonance Scattering in Chaotic Systems

Condensed Matter Physics

Optics

Extreme Eigenvalues of Wishart Matrices and Entangled Bipartite System

Random Growth Models

Laplacian Growth

Financial Applications

Information Theory

Ribonucleic Acid Folding

Complex Networks

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